Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs

M. Shcherbina, B. Tirozzi

We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}{\sum }_{k=1}^n\exp \{-u{G}_{kk}(z)\}$ with $G(z)=(z-iA{)}^{-1}$. W…